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(3 − 0.1645, 3 + 0.1645) = (2.8355, 3.1645)
Question: what does the conﬁdence interval mean? “The probability that µ is in this
interval is 90%”? NO! Utku Suleymanoglu (UMich) Interval Estimation 7 / 17 Interval Estimation of Population Mean Interpretation of Conﬁdence Interval Estimates Population parameter, µ, is unchanging. It is not probabilistic.
Once you build an interval with the single x at hand, µ is either inside or outside of
¯
it. You don’t know which is the case, but there is no probability to it.
So you don’t say “probability that µ is in my CI (2.8355, 3.1645) is 90%”.
Correct interpretation of CI’s are related to sampling distributions. Notice L and U
¯
are also functions of X , hence also random themselves.
We build diﬀerent CI’s with diﬀerent x ’s if we had diﬀerent samples.
¯
We had kept doing this (repeated sampling), we know that 90% of the CI’s we build
will have the correct µ in it.
That is why 100(1 − α)% is called the conﬁdence level. NOT because we have 90%
probability that µ is inside of the conﬁdence interval we just built.
But we are 90% co...
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 Spring '08
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